Notice that how the implied covariance structure of the data is determined by the coefficient matrices ( i.e. \(\mathbf {B}\) , \(\mathbf {C}\) , and \(\mathbf {W}\) ) and the covariance matrices (i.e. \(\Psi \) , \(\Phi _{z_1}\)  and \(\Phi _{\xi }\) ). More importantly, notice also that an SEM model implicitly assumes that the relationships between the observations are linear since covariances are measures of linear association. Another aspect of SEM models that is worth pointing out is that although we can assess whether a particular implied decomposition is consistent with the data, we cannot determine whether it is the only decomposition that is equally consistent with the data. That is, the same data can be generated given different latent structural relations [1]}.
